in a medium bowl, combine the chocolate, water, and butter. Warm the mixture in the microwave for 15 seconds at a time, stirring between each time, until the chocolate is melted and smooth. Set aside to cool.
In the bowl of a standing mixer, beat the egg yolks at medium high speed until just combined (10 to 15 seconds).With the mixer still running, add about half of the sugar. Continue beating, scraping the bowl as needed, for 8 minutes. Stir int he vanilla, then transfer the yokk mixture to a large bowl.
In the clean bowl, beat the egg whites and cream of tartar at medium speed until foamy (about 30 seconds). Add 1 tablespoon of sugar and continue beating until soft peaks form, then gradually add the rest of the sugar. Beat until the whites are glossy and hold stiff peaks (about 1 minute). Do not overbeat.
Stir the chocolate mixture into the egg yolks. Once combined, add about 1/4 of the egg whites to the chocolate mixture, and gently fold it in with a rubber spatula. Fold in the remaining egg whites until combined, then sprinkle the dry ingredients over the top. Quickly and gently fold them in until combined.
Once the cake is done, overturn it onto the prepared towel, peel away the parchment, and immediately roll the short side of the cake up in the towel. Transfer the roll to a wire cooling rack and allow to cool for at least 15 minutes.
Assemble the cake: Once cooled, unroll the cake and spread the jam over the surface, leaving a 1-inch border around the edge. Next, spread about 1 cup of whipped cream over the top of the jam. Sprinkle with the blackberries, and re-roll the cake. Trim both ends using a serrated knife. Drizzle with ganache and garnish with remaining blackberries.